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Home , Classical genetics, Mendelian inheritance

Chapter 2. The beginnings of Genomic – Classical Contents

2. The beginnings of Genomic Biology – 2.1. Mendel & Darwin – traits are conditioned by  CHAPTER 2. THE BEGINNINGS OF GENOMIC 2.2. Genes are carried on 2.3. The chromosomal theory of inheritance BIOLOGY –CLASSICAL GENETICS 2.4. Additional Complexity of 2.4.1. Multiple 2.4.2. Incomplete and co-dominance 2.4.3. Sex linked inheritance 2.4.4. It should be clear that the beginings of genomic 2.4.5. 2.5. Genes on the Same are Linked biology are grounded in classical or Mendelian Genetics. 2.5.1. : chromosomes assort independently Once the relationship between traits and genes was 2.5.2. Mapping genes on chromosomes understood, the relationship between cells and genetics 2.6. : Traits that are Continuously Variable was investigated, leading to the discovery of 2.7. : Traits in groups of individuals chromosomes, and a quest for the substance that carried the genetic information began, culminating in the discovery of DNA. These studies constitute the contribution of classical genetics to the founding of the genomic era.

CONCEPTS OF GENOMIC BIOLOGY Page 1 In 1859 published his book On the (RETURN) Origin of Species. In this work Darwin described a mass of descriptive support for the concept that 2.1. MENDEL & DARWIN – “traits” are stably transmitted through subsequent TRAITS ARE CONDITIONDBY GENES. generations, and that organisms that have superior traits survive their natural environment to pass those The idea of genomic biology begins with a traits on to the next generation. However, Darwin did consideration of what makes up . not describe any mechanism for such transmission of Specifically what are genes. The timeline of genetics traits to the next generation. and begins with the early work of Charles Experimental evidence for a mechanism explaining Darwin and who didn’t really talk how traits pass to subsequent generations came in about genes per se, but who did describe the 1866 when an Austrian monk, Gregor Mendel, behavior of the characteristics of biological published his studies covering 10 years worth of work organisms, which they referred to as traits. on the mechanism of inheritance of 7 characteristics in garden in a paper called “Experiments in Plant Hybridization”.

Charles Darwin Gregor Mendel CONCEPTS OF GENOMIC BIOLOGY Page 2  The law of independent segregation. Inherited characteristics (such as stem length in Mendel's plants) exist in alternative forms (tallness, shortness)—today known as alleles. For each characteristic, an individual possesses two paired alleles—one inherited from each parent. Correspondingly, these pairs segregate (i.e. separate or assort) in germ cells and recombine during reproduction so that each parent transmits one

to each offspring. Mendel's Experiments Video  The law of independent assortment. Specific traits In 1865 Mendel delivered two long lectures that operate independently of one another. A pea plant might have a stem that is tall or short, but in either were published in 1866 as "Experiments in Plant case may produce or gray coats. Hybridization." This established what eventually became formalized as the Mendelian Laws of However, the significance of Mendel’s work and his inheritance: insight into the mechanism of inheritance went unrecognized until 1900 when three European  The law of dominance. For each trait, one factor scientists, , , and Erich von () is dominant and appears as the in Tschermak reached similar conclusions in their own the first filial generation (F1). In the F2 generation the dominant trait occurs more often, in a definite 3:1 research though they claimed to be unaware of ratio. The alternative form is recessive. In Mendel's Mendel’s earlier theory of the 'discrete units' on peas, tallness was dominant, shortness recessive. which genetic material resides. Therefore, three times as many plants were tall as The biological entity (factor) responsible for were short. This constant ratio represents the random defining traits was later termed a gene by Wilhelm combination of alleles during reproduction. Any Johansen in 1910, but the biological basis for combination of alleles that includes the dominant inheritance remained unknown until DNA was allele will express that form of the trait. identified as the genetic material in the 1940s. Thus,

CONCEPTS OF GENOMIC BIOLOGY Page 3 it was early in the 20th century that the name “gene” American graduate student, in 1902 at about the same was given to the hereditary unity described by time that Mendel’s Laws of inheritance were being Mendel decades earlier, and the study of genetics and rediscovered. genomics began in earnest. The developing theory stated:

(RETURN)  More than one gene is located on each chromosome. 2.2. GENES ARE CARRIED ON CHROMOSOMES. Thus, chromosomes are like a string of beads with each gene represented as a bead. Along the length of At about the same time that genes were coming the chromosome (string of beads) there are genes for into focus as having a role in inheritance, a series of many traits on each chromosome, and each gene observations at the cellular level established: occupies a specific position on each chromosome  The existence of structures called chromosomes. called a .  The chromosomes are passed from one generation to the next and carry genes to the next generation as they are passed. These points were incorportated into what we now know as the Chromosomal Theory of Inheritance.

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 Chromosomes carry genes. The notion that Mendel’s particulate hereditary factors reside on visible structures called chromo-somes was originally independently proposed by Theodor Boveri, a German scientist, and , an CONCEPTS OF GENOMIC BIOLOGY Page 4

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2.3. THE CHROMOSOMAL THEORY OF INHERITANCE.

In the early years of the 20th century , who was skeptical about the theories of the day concerning Mendel’s observations and the role of chromosomes in inheritance, began conducting a series of experiments using the fruit fly, Drosophilla melanogaster, that ultimately convinced him of the details of inheritance leading to what is called today Figure 2.1. The complete set of 23 pairs of human chromosomes is shown in the karyotype above. Note the chromosomal theory of inheritance. The general that there are 22 pairs of autosomal Chromosomes, and tenets of this theory are given below: the X and Y sex chromosome “pair”. Thus, we say that there are 22 pairs of homologous autosomal  Multiple genes conditioning the cellular and chromosomes plus a pair of sex chromosomes (X or Y) organismal traits an organism possesses are passed in humans, and humans have 46 (diploid number) from one cellular or organismal generation to the next chromosomes in total.

on chromosomes.

 Genes for specific traits reside at specific positions on chromosomes called loci (singular locus). The complete set of human chromosomes is shown in Figure 2.1. Humans have 22 pairs of autosomal

 Most cells of an organism have homologous pairs of chromosomes, and the X and Y sex chromosomes that chromosomes for each chromosome found in the . are present in males (XY) of females (XX). Thus, we say  The complete set of chromosomes an organism that there are 22 pairs of homologous autosomal possesses is called it’s karyotype. chromosomes plus a pair of sex chromosomes (X or Y) in humans. Humans have 46 chromosomes in total, and the diploid number of chromosomes is 26.

CONCEPTS OF GENOMIC BIOLOGY Page 5 , eukaryotic cells that pass chromosomes to the next organismal generation, contain only a haploid number of chromosomes (23 in the case of  The that an organism possesses in homans). Thus, gametes have only 1 chromosome combination with environmental factors is responsible from each pair found in a non-gametic cell. for production of the trait that we see. This is also a Chromosome numbers are constant for a species, but definition of the phenotype of an individual, i.e. the vary from one species to another. appearance of the individual resulting from the interaction of genotype and environmental factors.  One of the chromosomes in each homologous pair Thus, an organism can demonstrate a dominant comes from the maternal parent while the other phenotype or a recessive phenotype. chromosome in the pair comes from the paternal

parent.  Although traits are conditioned by genes at specific What Mendel observed was the phenotype of his loci on the chromosomes, the gene at a given locus pea plants. From observations of phenotype he coming from each parent may not be the same. They proposed a model for genotypic behavior of his can be either the dominant (according to Mendel’s law “factors” that we no know as genes. We also know of dominance) factor, ort he recessive factor. We now that these genes reside on chromosomes, and the call the nature of the factor (gene) at each locus, an manner in which the chromosomes are passed to the allele. next generation provides the basis for Mendel’s law  When both the maternal and paternal homologous of segregation that directly relates the behavior of the chromosome contain the same allele, the organism is chromosomes bearing the genes to the phenotypic said to be homozygous, but if the alleles contained at the locus on the homologous chromosomes are behavior that Mendel observed. However, there are different the organism is said to be heterozygous. a number of instances where, although Mendel’s law of segregation applies additional background is  When an organism is homozygous, if the allele it bears is the dominant allele, the organism demonstrates a required to appreciate how such Mendel’s work homozygous dominant genotype. While a applies.

homozygous organism bearing 2 identical recessive alleles is considered homozygous recessive genotype. (RETURN)

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2.4. ADDI TIONAL COMPLEXITY OF MENDELIAN 2.4.1. Multiple alleles (retrun) INHERITANCE. (RETURN) Note that it is possible that for some traits more than 2 alleles exist. In this case there is a hierarchy of Once the simple laws of Mendel that governed dominance among the multiple alleles. In any given inheritance had been established and related to the individual the more dominant allele of the 2 alleles it behavior of chromosomes, there were many posses is dominant, while the more recessive one will examples of situations that were not fully accounted be the recessive allele. th for with the simple laws. In the early 20 century Examples of this phenomenon could be the ABO there was great controversy, not just about the blood type system and the rabbit coat color example chromosomal theory and its relationship to inheritance of traits, but about other known examples discussed shown in Figure 2.2. There are 4 unique that appeared not to be explained by Mendel and the alleles that have been found at the C-locus, which is chromosomal theory. one of 5 separate genetic loci that generate coat color Resolution of these issues took decades and patterns in rabbits. The hierarchy of dominance that required careful, thorough and well-designed has been observed at the C-locus suggests that the experiments too provide us with an understanding of wild type “large C” allele is the “most” dominant of many of these situation. In fact a few of these the alleles in the dominance hierarchy, and the “most controversies were not fully resolved until the recessive” of the alleles is the “small c” locus. A genomic era and some are still being investigated today. rabbit whose genotype is cc has an albino phenotype while a rabbit with a CC genotype will be fully colored (e.g. agouti, or black that is really dark grey as described in the Figure 2.2). The second most dominant allele is the chinchilla allele, cch- allele, and the ch-allele is intermediate in dominance between the cch- allele and the c- allele. Figure 2.2. Phenotypic description of the alleles of the C-locus for coat (RETURN) color in rabbits. Note that this patterning is also found in many other animals although the names of the may differ.

CONCEPTS OF GENOMIC BIOLOGY Page 7 2.4.2. Incomplete dominance and co-dominance A. Parents (retrun) Rr rr

It is also possible to have 2 alleles demonstrate an RR rr F1 intermediate phenotype in the heterozygous condition. This phenomenon is referred to as incomplete dominance (similar to co-dominance), Rr Rr rr rr

and can be observed in Figure 2.2. where the Rr Rr Rr Rr ch h ch phenotype of a c c or c c heterozygous rabbit is B. Parents

distinct and intermediate between the homozygous Rr rr (more) dominant cchcch and the homozygous (more) Rr Rr recessive chch or cc phenotypes. F1 Another example is given in Figure 2.3., where

pure breeding (homozygous) red and white flowered Rr Rr rr rr

plants are crossed to give rise to intermediate RRRr RrRr Rrrr rrrr heterozygous pink plants. In some plants the C. Parents

intermediate heterozygotes appear as separate Rr rr distinct patches of color. This is typical of the Rr rr description of co-dominant traits where the distinct F1 alleles in a heterozygote are both visible. Thus, co- dominance and incomplete dominance may be a Rr Rr rr rr distinction without a difference. Rr Rr rr rr Rr Rr rr rr (RETURN) Figure 2.3. Example of incomplete dominance in flower color of four o’clocks. A) Red flowering x White flowering yields all pink flowers; B) pink flowering x pink flowering yields 1 red : 2 pink : 1 while flowers; and C) pink flowering x white flowering yields half pink and half white flowers.

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2.4.3. Sex linked interitance (retrun) Another example that differs from typical Mendelian inheritance is sex-linked inheritance. In organisms that have X and Y choromosomes, such as Drosophila and humans, the female typically has a pair of X chromosomes (XX) while the male has an X and a Y chromosome (XY). So when a red-eyed female fruit fly is crossed with a white-eyed male, the result is all red-eyed progeny. This might seem like a normal autosomal inheritance pattern where red eyes are a dominant trait. However, in the reciprocal cross (a white-eyed female crossed to a red- eye male. All females will have red eyes, and all males will have white eyes. This demonstrates that the eye-color trait in Drosophilla is a sex-linked trait, and it is conditioned by a gene located on the X chromosome. Males contribute an X-chromsomes only to their daughters, as their sons must get the Y-chromosome. Females contribute their X-chromsomes to both males and Figure 2.4. Demonstration of sex linked inheritance. The outcome as females. demonstrated in the Punnet’s squares above is different based on whether the male bears the dominant or recessive trait. This phenomenon is pictorially demonstrated using Punnet’s squares in Figure 2.4. below. (RETURN)

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2.4.4. Epistasis (retrun) 2.3.5. Epigenetics (retrun) Sometimes the phenotype of an organism does not More recently discovered phenomena involving reflect the actual genotype. This can be the case heritable changes in that are not when one or more genes are epistatic to others. related to actual changes in DNA sequence, but rather Epistatic genes modify or eliminate the phenotype of are related to chromosome structure and function others so that the phenotype is not apparent. An have also emerged. These phenomena are referred example of an epistatic gene might be a gene for to as epigenetic inheritance, and have emerging baldness. This gene would be epistatic to genes for importance in virtually all areas of biology and hair color, e.g. red hair or blond hair genes. medicine. We will discuss them in greater molecular Another example of an epistatic gene is the c-allele detail later, but they clearly had their beginning in in rabbits given above. This allele produces a classical genetics.

phenotypically albino, white rabbit with pink eyes in (RETURN) the homozygous recessive state. However, there are at least 5 additional genetic loci that condition various coat colors and patterns. Many of these other loci have multiple alleles (as does the C-locus, see above), but the rabbit will be albino if it is genotypically cc (homozygous recessive) at the C-locus. Demonstrating that the C-locus is epistatic to the other coat color loci.

CONCEPTS OF GENOMIC BIOLOGY Page 10 (RETURN) chosen 7 genes on 7 different chromosomes to work with, and as a consequence Mendel’s law of 2.5. GENES ON THE SAME CHROMOMSOME ARE independent assortment did not necessarily apply to all LINKED. genes since it was the chromosomes that assorted not the genes per se. In his studies with garden peas Mendel observed that The question has been raised as to whether Mendel each of the 7 traits that he studied behaved chose only data to work with that supported this independently of each other. The mechanism that this theory and disregarded other data or traits that did not observation generated involved genes (hereditary fit his theory to present. Whether this is true or not we factors) assorting independently of each other. Thus, will never really know, but it surely doesn’t detract when 2 factors (genes) were involved in a cross, each of from the important contribution Mendel’s work has them behaved independently. made to the of genetics and genomic biology However, the chromosomal theory of inheritance by establishing an important set of rules that govern contradicts this observation by suggesting that genes the inheritance of traits. are linked together on chromosomes, and further suggests that it is the chromosomes that are passed to 2.5.1. Meiosis: chromosomes assort the next generation. If this is the case, how can genes independently (retrun) on the same chromosome assort indepen-dently? The theory that allows us to explain the mapping of Answering this question plagued the early develop- genes begins with an understanding of the behavior of ment of genetics until the chromosomal theory of chromosomes during meiosis. During the assorting of inheritance emerged and the idea of gene linkage for diploid chromosomes sets like those found in somatic genes on the same chromosome were clearly shown by cells into haploid chromosomes sets like those found in Thomas Hunt Morgan and his colleagues about a gametes, it is possible to exchange parts of century ago. chromosomes between different homologous sister chromatids. Once established that it is chromosomes that assort independently, it was clear that Mendel had fortuitously CONCEPTS OF GENOMIC BIOLOGY Page 11 The process of meiosis begins with a diploid cell containing 2 copies of the complete diploid (diploid set of chromosomes) and ends with 4 cells containing 1 copy of the haploid genome (haploid set of chromosomes). In the first meiotic division (meiosis I) homologous chromosomes each consisting of 2 sister chromatids are separated from each other to produce 2 haploid cells with each chromosome consisting of 2 sister chromatids. As these chromosomes (chromatids) align at the mid-plane of the cell in late prophase I of meiosis, the chromatids of homologous chromosomes may overlap with each other and pieces of each chromosome are sometimes exchanged. This process is called crossing over or . Once this exchange has taken place and meiosis I is completed, the exchanged chromosomes become part of new separate haploid chromosome sets in each of 2 haploid cells. Each of these cells undergoes a second meiotic division where the sister chromatids are separated, leading to 4 cells which have a unique combination of traits that mixed the traits derived from each parent of the original individual. Since this process is taking place Figure 2.5. The stages of meiosis I and meiosis II are shown. This on each chromosome of the organism, the end result is involves two separate cell divisions that lead to the formation of 2 a likelihood that every consists of a genome haploid cells from one diploid cell. that is unique compared to the parental genomes that CONCEPTS OF GENOMIC BIOLOGY Page 12 produced the individual. This mixing of genes at loci chromosomes can be exchanged during meiosis, the along the length of chromosomes contributes much to frequency of this exchange provides a measure of the the required to make the process of relative distance between linked genes on the same work. chromosome. Distantly located genes recombine more frequently while nearby genes rarely recombine and are 2.5.2. Mapping genes on chromosomes (retrun) closely linked. By measuring the frequency of crossing- Using Drosophila, Thomas Hunt Morgan and his over between linked genes on the same chromosomes students accumulated a large collection of mutants the distance between genes can be estimated, and (allele pairs) for specific traits. As the collection of genetic maps can be calculated and constructed. mutants grew, it became clear that particular sets of From Morgan and Sturtevant’s work, the percentage traits assorted together rather than independently as crossing-over became a chromosomal distance Mendel had found with his peas. Morgan concluded measurement, and the definition of a unit of crossing that genes for specific traits are linked together into 4 over, became know as the Centimorgan (=1% crossing groups in Drosophila. This happened to equal the over between linked genes on the same chromosome). number of chromosomes observed in Drosophila cells in the microscope. By studying the process of meiosis as described above, it was further established that pieces of homologous chromosomes are exchanged when chromosome numbers are reduced from 2 homologous chromosomes per cell, to just a single chromosomal homolog in the gametes that are fused to produce the next generation. Figure 2.6. Alfred Sturte- From this initial idea of linkage of genes into groups vant’s first genetic map of on chromosomes, , Morgan's student, the Drosophila chrom- osomes. was the first scientist to make genetic or linkage maps of fruit fly chromosomes. To do this Sturtevant reasoned that since pieces of homologous CONCEPTS OF GENOMIC BIOLOGY Page 13 In the human population there are not discrete 2.6. QUANTITATIVE GENETICS: TRAITS THAT ARE height classes. Height varies between over 7 feet tall CONTINUOUSLY VARIABLE. to under 4 feet tall in the human population; there are not such things as pure breeding lines of tall Mendel, perhaps fortuitously, chose to work with a people and short people similar to what Mendel series of traits where he could find a pair of discrete developed in pea plants, and when two extremely tall phenotypes. However, not all phenotypes are so clean individuals are mated, the progeny, though perhaps producing discrete classes. Above we have already taller than average, are not all extremely tall like their looked at examples of incomplete dominance, multiple parents. Traits such as tallness are often referred to alleles, and epistasis, but for other traits phenotypes as quantitative traits, and a separate branch of are continuously variable between 2 extremes rather genetics called quantitative genetics has emerged to than producing discrete phenotypic classes. Examples study and understand quantitative phenomena. of such traits are often related to height, weight, or amounts of things. There are several books written on the topic of quantitative inheritance, and one can link- out to online more brief treatments of the topic can be found. A number of additional references on quantitative genetics can be found at the link-out, but be aware that these may not be adequately edited, and they are certainly incomplete, although they do provide an overview of the area suitable for understanding the relationship of quantitative genetics to genomic biology. Also note that there are many more complex issues involved in understanding Figure 2.7. Description of a quantitative locus. A gene contributes “d” average effect, but the value obtained lies quantitative inheritance that require statistical between +a and –a away from d. background beyond that expected here.

(RETURN) CONCEPTS OF GENOMIC BIOLOGY Page 14 In classical genetics, statistical approaches to In addition to statistical treatments of quantitative quantitative inheritance have emerged that provide inheritance it is also widely considered that statistical tools for detailed analyses of quantitative quantitative inheritance results from the interaction inheritance. These statistical approaches focus on of a number of different loci where each of these has phenotypically defining 2 alleles at a putative an effect on the final integrated outcome. This is “quantitative locus”. The midpoint between termed polygenic inheritance. homozygotes of the 2 alleles is defined as +d, and the each opposing homozygotes would phenotypically deviate from the midpoint by +a or –a (see Figure 2.7.). In a heterozygote a phenotype closer to the homozygous dominant (+a) than the midpoint (+d), indicates a dominant character to that allele, and a heterozygous phenotype closer to the homozygous recessive (–a) results from a less dominant character to the dominant allele. A measure of the heterozygote distance from the midpoint then becomes a statistical definition of incomplete dominance for such a quantitative gene. Note that in Mendel’s tall versus short pea plants the phenotype of the heterozygote is almost precisely +d, indicating 100% dominance of the cM tall allele over the short allele. In actual fact it is even Figure 2.8. Mapping quantitative trait loci using LOD scores. possible to have a super dominant allele that gives a This quantitative analysis identifies quantitative trait loci (QTLs) located on various chromosomes and shows which regions of heterozygous phenotype more distant from the the chromosome contribute significant genes to the quantitative midpoint than +a, a phenomenon that is sometimes phenotype being investigated. The figure compares the severity referred to as vigor. of an arthritic phenotype in hip and spine by location on the chromosome.

CONCEPTS OF GENOMIC BIOLOGY Page 15 are nonallelic genes at a set of loci (RETURN) distributed in the genome that contribute to the 2.7. POPULATION GENETICS. (RETURN) overall quantitative phenotype observed in the

organism. Figure 2.8 above shows how phenotypic data and their proximity to known marker genes Statistical genetic theories have also become a allows the mapping of chromosome regions major consideration in the discipline of population influencing quantitative phenotypes referred to as genetics. In the context of a population, the quantitative trait loci (QTLs). The distance measure frequency of individuals having a given genotype is used in this map is the so-called LOD score that related to the frequency of each allele in the breeding relates phenotype to position on the chromosome. population. If you assume that mating in a population The LOD score method of locating regions of is random and very large to assure that it is chromosomes that influence quantitative inheritance homogeneous, then the frequency of in relies on having numerous closely related genetic the subsequent generation will be directly related to markers on chromosomes. the frequency of alleles in the gamete pool that Although the method has been available for some produces that generation. Thus, where there are only time, the advent of genomic techniques for identifying and mapping DNA sequence markers on TABLE 2.1. chromosomes has markedly improved the accuracy Female gametes Gamete / R / p r / q

and facility of identifying QTLs in genomes. Frequency

e

e 2 l

Additionally, the availability of complete genome s R / p RR / p Rr / pq

a

m

e t

a 2 M sequences makes it possible to not only identify g r / q Rr / pq rr / q regions of the chromosome related to phenotypes, but to actually identify the specific causally-related genes. The QTL approach has found wide application 2 alleles for a given locus found in the population, and ranging from the mapping of human disease QTLs (example in Figure 2.8), to applications in plant and p = frequency of dominant allele gametes while q = animal breeding, and to application in evolutionary frequency of the recessive allele gametes, p + q = 1. and population genetics among others. As is shown in table 2.1., the

CONCEPTS OF GENOMIC BIOLOGY Page 16 frequency of homozygous dominant individuals in the occurring in the population and that there be no population should be p2 and the frequency of taking place for the alleles or linked homozygous recessive individuals will be q2. genes in question. Additionally, there should be no Heterozygotes should then be found at a frequency of (migration into or from the population) 2pq, and in total p2 + 2pq + q2 = 1. This is the binomial taking place, and the population should not have expansion of (p + q)2. gone through a dramatic change in size recently that If this looks familiar, recall the Punnett’s squares may have related to in the population. It that we did showing gene segregation in the F-2 should also be noted that the equations given above generation. In that case since heterozygotes produce relate only to diploid species. Some species found in gametes, half of which carry the dominant allele and nature are natural polyploids (having more than 2 half of which carry the recessive allele, i.e. p = q = 0.5. sets of chromosomes), and the equations for Substituting these gamete allele frequencies into the describing the behavior of polyploids are different binomial equation above, we get the 1:2:1 from the bionomial expansions described above. Also segregation ratios we expect. other changes in the equations are required for situations where there are more than 2 alleles found However, in a population, where there are both in a population. homozygotes and heterozygotes all producing gametes, p will not usually equal q, and a different As was with quantitative genetics, the introduction equilibrium of gametes and genotypes will be of tools from genomic studies into population established and maintained through time. This genetics have greatly facilitated the investigation of description is called a Hardy-Weinberg equilibrium. genes in populations, and this is particularly relevant in the investigation of the human population. In order for a population to sustain a Hardy- Population genetic studies using molecular markers Weinberg equilibrium additional factors for important health-related genes are now common (assumptions) must be in place or the equilibrium will place in Public Health studies. not be maintained. In addition to a large population and random mating within the population as (RETURN) discussed above, it is also necessary that there be no